How long are the tag ends?
I can sometimes have a momentary hang if i leave an 8th
or even 16th of an inch tag end.
Tighten the knot as much as you can, then cut as close as
you can. When I have tied a good double-uni, I don't hang
much at all. Love that knot. Also use the Mod'd Albright, aka
Alberto. Cinched down well, tag cut close, excellent knot.
And like @OkobojiEagle said, smaller diameter lines will help,
if you can use 'em. I use 10, 15, and 20# braid and tie leaders
up to 15#. Usually no issues with either double-uni, and really
no issues with Mod'd Albright/Alberto.